2 tablespoons all-purpose flour
1 teaspoon black pepper
2 tablespoons paprika, divided
2 1/2 teaspoons kosher salt, divided
1 (2-lb.) boneless chuck roast, trimmed and cut into 1-in. cubes
2 tablespoons olive oil
1 1/4 cups chopped yellow onion (from 1 medium onion)
1/2 cup finely chopped celery (from 3 stalks)
1/2 cup finely chopped carrots (from 2 medium carrots)
2 large garlic cloves, minced (1 Tbsp.)
1 (14 1/2-oz.) can fire-roasted diced tomatoes (such as Muir Glen Organic), undrained
1 1/2 tablespoons red wine vinegar
12 ounces uncooked egg noodles
Stir together flour, pepper, 1 tablespoon of the paprika, and 2 teaspoons of the salt in a large bowl; add beef cubes, and toss to evenly coat. Heat oil in a large skillet over medium-high. Add half of the beef; cook until well browned on both sides, about 4 minutes per side. Transfer to a 5-to 6-quart slow cooker. Repeat process with remaining beef. Reserve drippings in skillet and any remaining flour mixture in bowl.
Add onion, celery, carrots, and garlic to drippings in skillet; cook over medium, stirring often, until softened, about 2 minutes. Add tomatoes, reserved flour mixture in bowl, and remaining 1 tablespoon paprika; cook, stirring constantly, 1 minute. Transfer mixture to beef in slow cooker.
Cover slow cooker; cook on HIGH until beef is fork-tender and sauce has thickened, about 4 hours. Remove from heat; stir in vinegar and remaining 1/2 teaspoon salt. During final 10 minutes of goulash cooking, prepare egg noodles according to package directions. Serve goulash over hot egg noodles.